establish identity

sec 0/1 + sec0 = 1 - cos0/sin^2 0

Do you mean sec 0/(1 + sec 0) ?

On the right side,do you mean
(1 - cos 0)/sin^2 0?

You need to use parentheses to make your equations unambiguous.

To establish the identity sec(0/1) + sec(0) = (1 - cos(0)) / sin^2(0), we will simplify the left-hand side of the equation and then simplify the right-hand side of the equation.

Starting with the left-hand side:

sec(0/1) + sec(0)

The secant function is the reciprocal of the cosine function, so sec(θ) = 1 / cos(θ).

Therefore, we can rewrite the left-hand side as:

1 / cos(0/1) + 1 / cos(0)

Now, cos(0/1) is equivalent to cos(0), which is equal to 1. Similarly, cos(0) is also equal to 1.

Substituting these values, we get:

1 / cos(0) + 1 / cos(0)

Since both terms are equal, we can combine them:

2 / cos(0)

Using the identity cos(θ) = 1/sec(θ), we can simplify further:

2 / cos(0) = 2 / ( 1 / sec(0) ) = 2 × sec(0)

Therefore, the left-hand side simplifies to:

2 × sec(0)

Now, let's simplify the right-hand side of the equation:

(1 - cos(0)) / sin^2(0)

Since cos(0) is equal to 1, we have:

(1 - 1) / sin^2(0)

Simplifying further:

0 / sin^2(0) = 0

Now, let's compare the simplified left-hand side and right-hand side:

2 × sec(0) = 0

From here, we can see that the two sides are not equal. Therefore, the given equation sec(0/1) + sec(0) = (1 - cos(0)) / sin^2(0) is not an identity.